Making grooves in objects
I would start over completely and create the topology in 2D first, in all quads, tracing the reference image.



(Sorry for the two-billion pixel screen shots. You can thank retina display.)

Anyway, if you make topology like this you can get the curves you're hoping to achieve without cutting.

Consider this a starting point, and also just an example of one possible way you could do it.

Note the tightly-spaced holding loops around the curves that add sharpness. These also serve as a buffer between those curves and the 5-poles in some spots:



Above: A 5-pole (marked in red) buffered by a holding loop (green).

As you've probably noticed, more closely-spaced holding loops create sharper edges.



Above: A more widely-spaced loop (green) will create softer edges, while a more tightly-spaced loop (orange) will create sharper edges.

Topology is a broad topic, but it's just about collecting different techniques, and adjusting how you think about shapes. It's half art form and half math. Stick with it.